Trying to wrap this mesh mask to another mesh
You were on the right track when trying to use the Shrink-wrap modifier. All you need to do Is fiddle with some settings. 

All you have to make sure is that you select the "Project" mode and tick both of the "Direction" boxes (this tell blender which normal to project, ticking both is just easy). Then you're going to want to increase the offset just a little bit so your projected mesh doesn't intersect too badly with your head.



I see the mesh you'd like to project looks like its got 3 dimentionality, so if you want to preserve that, I suggest you remake it with splines and add a skin modifier to it.